In almost every practical scenario in which an image is being captured by a camera, the light reflected from a surface is scattered in the atmosphere before it reaches the camera. This may be due to the presence of aerosols, such as dust, mist, and/or fumes, which deflect light from its original course of propagation. In long distance photography or foggy scenes, this process can have a substantial effect on the image, in which contrasts may be reduced and surface colors may become faint. Such degraded photographs often lack visual vividness and appeal, and moreover, they may offer a poor visibility of the scene contents. This effect may be an annoyance to amateur, commercial, and/or artistic photographers, as well as undermine the quality of underwater and/or aerial photography. This may also be the case for satellite imaging, which is used for many purposes including, for example, cartography and web mapping, land-use planning, archeology, and/or environmental studies.
As discussed in more detail below, in this process light, which should have propagated in straight lines, is scattered and replaced by previously scattered light, called the “airlight” (See Koschmieder, H., “Theorie der horizontalen sichtweite,” in Beitr. zur Phys. d. freien Atm., 171-181, 1924, hereinafter “Koschmieder 1924,” the contents of which are hereby incorporated herein by reference in their entirety). This can result in a multiplicative loss of image contrasts, as well as an additive term due to this uniform light. As described in more detail below, a model that is commonly used to formalize the image formation in the presence of haze factors the degraded image into a sum of two components: the airlight contribution and the unknown surface radiance. Algebraically these two, three-channel color vectors are convexly combined by the transmission coefficient, which is a scalar specifying the visibility at each pixel. Recovering a haze-free image using this model requires the determination of the three surface color values, as well as the transmission value at every pixel. Since the input image provides three equations per pixel, the system is ambiguous and the transmission values cannot be determined. A formal description of this ambiguity is described below. However, intuitively it follows from the inability to answer the following question based on a single image: are we looking at a deep red surface through a thick white medium, or is it a faint red surface seen at a close range or through a clear medium. In the general case, this ambiguity, which is referred to as the “airlight-albedo ambiguity,” holds for every pixel and cannot be resolved independently at each pixel given a single input image.
A need, therefore, exists, for a technique for resolving this ambiguity and, as a result, de-hazing a captured image, using only the information obtainable from the captured image itself.